diff --git a/books/bookvol2.pamphlet b/books/bookvol2.pamphlet
index da71de9..302dc0c 100644
--- a/books/bookvol2.pamphlet
+++ b/books/bookvol2.pamphlet
@@ -377,7 +377,111 @@ Roland Backhouse and Marcel Bijsterveld
``Category Theory as Coherently Constructive Lattice Theory''
November 1994
-\chapter{Implementation Details}
+\section{Terms to Understand}
+
+Suppose we wish to join Complex with Polynomial(Integer).
+What would elements of this combination look like?
+
+The union of the two is a co-product of topological spaces.
+
+The simple combination is not simply adding elements since
+\[i + x^2\]
+is not a valid combination.
+
+We need the algebraic co-product, known as the tensor product.
+We end up with a domain of Complex(Polynomial(Integer)).
+
+\begin{verbatim}
+-> a:Complex(POLY(INT)):=%i+3*x
+
+ 3x + %i
+ Type: Complex(Polynomial(Integer))
+-> a::POLY(COMPLEX(INT))
+
+ 3x + %i
+ Type: Polynomial(Complex(Integer))
+\end{verbatim}
+
+\section{Category Definition}
+A category has four parts.
+We need a set of objects, usually represented as dots.
+We need a set of arrows (maps, morphisms), from dot to dot.
+We need a way to compose arrows in an associative manner.
+We need an identity arrow from a dot to itself.
+
+The set of all arrows from dot A to dot B is written as $Hom_c(A,B)$
+or, sometimes $C(A,B)$. Notice that the set $C(A,B)$ is disjoint from
+$C(A,D)$ since each arrow has a unique domain and co-domain.
+
+For the example of the category Set, the objects are sets and the
+arrows are functions between sets.
+For the category Ring, the objects are rings and the arrows are ring
+homomorphisms.
+Similarly for the category Group, the dots are groups and the arrows
+are group homomorphisms.
+For a fixed Ring R, the category R-Mod has dots which
+are left R-modules and the arrows are R-module homomorphisms.
+We can also look at the category Mod-R which has dots of right R-modules
+and arrows which are R-module homomorphisms.
+For the category K, if K is a field, the dots are K-vector spaces and
+the arrows are K-linear transformations.
+
+In Axiom the dots are Types (such as Integer or Character) and the
+arrows are functions between them with signature:
+\begin{verbatim}
+ f : Integer -> Character
+\end{verbatim}
+
+Relations between categories is called a {\bf functor}.
+A functor F takes things in category C into things in category D.
+We need a function on objects which maps objects of C to objects of D.
+We need a function on arrows which take arrows of C to arrows of D.
+
+The categories C and D well defined structure.
+They have a domain and co-domain of arrows.
+They have identity arrows.
+There is a rule of composition of arrows. These form commutative diagrams.
+
+First we have to make sure the functor F maintains the domain and co-domain
+structure of C.
+When we apply functor F to C we need to preserve all of the structure
+so F has to be defined on all of these properties. If we look at two
+dots in category C and a function f which is an arrow in C
+\begin{verbatim}
+ f
+ A ----> B
+\end{verbatim}
+then the functor F has to operate on everything so we get:
+\begin{verbatim}
+ Ff
+ FA ----> FB
+\end{verbatim}
+This means that if $dom$ is the domain function in C then the functor
+F commutes with $dom$. That is, applying $F(dom(f)) = dom(F(f))$.
+
+Next we have to make sure the functor F maintains the identity arrow of C.
+From the above we know that $F(identity(x)) = identity(F(x))$.
+
+Finally we have to make sure that the rule for composition of arrows
+in C is preserved. So the functor F has to make sure that what composes
+in C also composes with the same diagram in D.
+
+Some standard functors are the identity functor $1_c$ which just maps
+C to C. We can form a functor which forgets properties so that the
+category Group could map to its underlying set. We can lift a category
+by forgetting properties, for example, lifting the category of Abelian
+Group C to Group D by ``forgetting'' the commutative property of C.
+Similarly the category Ring or the category Module can be mapped to
+the underlying Abelian Group. There is also the Constant functor which
+maps all of the dots in C to a single dot in D and all of the arrows in
+C to the identity arrow in D.
+
+The category CommutativeRing R can be mapped to a Group with the functor
+$GL_n$ which is the group of invertible NxN matrices with entries in
+the CommutativeRing R.
+
+
+\chapter{Axiom Implementation Details}
\section{Makefile}
This book is actually a literate program\cite{2} and can contain
executable source code. In particular, the Makefile for this book
diff --git a/changelog b/changelog
index 0925c8d..b5f35fa 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20130316 tpd src/axiom-website/patches.html 20130316.03.tpd.patch
+20130316 tpd books/bookvol2 category theory notes
20130316 tpd src/axiom-website/patches.html 20130316.02.tpd.patch
20130316 tpd buglist SOLVERAD fix 40043
20130316 tpd books/bookvol10.4 SOLVERAD fix 40043
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 02903b9..eee48bb 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -4073,5 +4073,7 @@ books/bookvol10.2 CLAGG fixed 40021
books/bookvol10.3 CHAR fix 40022
20130316.02.tpd.patch
books/bookvol10.4 SOLVERAD fix 40043
+20130316.03.tpd.patch
+books/bookvol2 category theory notes